Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 009, 11 pages      arXiv:0801.4728      https://doi.org/10.3842/SIGMA.2008.009
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

A Unified Model of Phantom Energy and Dark Matter

Max Chaves a and Douglas Singleton b
a) Escuela de Fisica Universidad de Costa Rica, San Jose, Costa Rica
b) Physics Department, CSU Fresno, Fresno, CA 93740-8031, USA

Received November 01, 2007, in final form January 22, 2008; Published online January 30, 2008

Abstract
To explain the acceleration of the cosmological expansion researchers have considered an unusual form of mass-energy generically called dark energy. Dark energy has a ratio of pressure over mass density which obeys w = p/ρ < −1/3. This form of mass-energy leads to accelerated expansion. An extreme form of dark energy, called phantom energy, has been proposed which has w = p/ρ < −1. This possibility is favored by the observational data. The simplest model for phantom energy involves the introduction of a scalar field with a negative kinetic energy term. Here we show that theories based on graded Lie algebras naturally have such a negative kinetic energy and thus give a model for phantom energy in a less ad hoc manner. We find that the model also contains ordinary scalar fields and anti-commuting (Grassmann) vector fields which act as a form of two component dark matter. Thus from a gauge theory based on a graded algebra we naturally obtained both phantom energy and dark matter.

Key words: dark energy; phantom energy; graded algebras.

pdf (238 kb)   ps (158 kb)   tex (17 kb)

References

  1. Dondi P.H., Jarvis P.D., A supersymmetric Weinberg-Salam model, Phys. Lett. B 84 (1979), 75-78, Erratum, Phys. Lett. B 87 (1979), 403-406.
    Ne'eman Y., Irreducible gauge theory of a consolidated Weinberg-Salam model, Phys. Lett. B 81 (1979), 190-194.
    Fairlie D.B., Higgs' fields and the determination of the Weinberg angle, Phys. Lett. B 82 (1979), 97-100.
    Squires E.J., On a derivation of the Weinberg-Salam model, Phys. Lett. B 82 (1979), 395-397.
    Taylor J.G., Electroweak theory in SU(2/1), Phys. Lett B 83 (1979), 331-334.
  2. Taylor J.G., Superunification in SU(5/1), Phys. Rev. Lett. 43 (1979), 824-826.
  3. Eccelstone R.E., A critique of supersymmetric Weinberg-Salam models, J. Phys. A: Math. Gen. 13 (1980), 1395-1408.
    Eccelstone R.E., The Weinberg angle in the supersymmetric Weinberg-Salam model, Phys. Lett. B 116 (1982), 21-22.
  4. Caldwell R.R., A phantom menace?, Phys. Lett. B 545 (2002), 23-29, astro-ph/9908168.
    Caldwell R.R., Kamionkowski M., Weinberg N.N., Phantom energy and cosmic doomsday, Phys. Rev. Lett. 91 (2003), 071301, 4 pages, astro-ph/0302506.
  5. Carroll S.M., Hoffman M., Trodden M., Can the dark energy equation-of-state parameter w be less than -1?, Phys. Rev. D 68 (2003), 023509, 11 pages, astro-ph/0301273.
  6. Riess A.G. et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astronom. J. 116 (1998), 1009-1038, astro-ph/9805201.
    Riess A.G. et al., The case for an accelerating universe from supernovae, Publ. Astronom. Soc. Pacific 112 (2000), 1284-1299, astro-ph/0005229.
  7. Perlmutter S. et al., Measurements of W and L from 42 high redshift supernovae, Astrophys. J. 517 (1999), 565-586, astro-ph/9812133.
  8. Zlatev I., Wang L., Steinhart P.J., Quintessence, cosmic coincidence, and the cosmological constant, Phys. Rev. Lett. 82 (1999), 896-899, astro-ph/9807002.
  9. Deffayet C., Dvali G., Gabadadze G., Accelerated universe from gravity leaking to extra dimensions, Phys. Rev. D 65 (2002), 044023, 9 pages, astro-ph/0105068.
  10. Deffayet C., Landau S.J., Raux J., Zaldarriaga M., Astier P., Supernovae, CMB, and gravitational leakage into extra dimensions, Phys. Rev. D 66 (2002), 024019, 10 pages, astro-ph/0201164.
  11. Kamenshchik A., Moschella U., Pasquier V., An alternative to quintessence, Phys. Lett. B 511 (2001), 265-268, gr-qc/0103004.
  12. Gonzalez-Diaz P.F., k-essential phantom energy: doomsday around the corner?, Phys. Lett. B 586 (2004), 1-4, astro-ph/0312579.
  13. Gonzalez-Diaz P.F., Axion phantom energy, Phys. Rev. D 69 (2004), 063522, 6 pages, hep-th/0401082.
  14. Sahni V., Dark matter and dark energy, Lect. Notes Phys. 653 (2004), 141-180, astro-ph/0403324.
  15. Bronnikov K., Scalar-tensor theory and scalar charge, Acta. Phys. Pol. B 4 (1973), 251-266.
    Ellis H., Ether flow through a drainhole - a particle model in general relativity, J. Math. Phys. 14 (1973), 104-118.
  16. Kodama T., General relativistic nonlinear field: a kink solution in a generalized geometry, Phys. Rev. D 18 (1978), 3529-3534.
    Armendáriz-Picón C., On a class of stable, traversable Lorentzian wormholes in classical general relativity, Phys. Rev. D 65 (2002), 104010, 10 pages, gr-qc/0201027.
    Lobo F.S.N., Phantom energy traversable wormholes, Phys. Rev. D 71 (2005), 084011, 8 pages, gr-qc/0502099.
    Sushkov S.V., Wormholes supported by a phantom energy, Phys. Rev. D 71 (2005), 043520, 5 pages, gr-qc/0502084.
  17. Cline J., Jeon S., Moore G., The phantom menaced: constraints on low-energy effective ghosts, Phys. Rev. D 70 (2004), 043543, 4 pages, hep-ph/0311312.
  18. Hannestad S., Mortsell E., Probing the dark side: constraints on the dark energy equation of state from CMB, large scale structure and type Ia supernovae, Phys. Rev. D 66 (2002), 063508, 5 pages, astro-ph/0205096.
    Melchiori A. et al., The state of the dark energy equation of state, Phys. Rev. D 68 (2003), 043509, 7 pages, astro-ph/0211522.
    Knop R.A. et al., New constraints on WM, WL, and w from an independent set of eleven high-redshift supernovae observed with HST, Astrophys. J. 598 (2003), 102-137, astro-ph/0309368.
    Spergel D.N. et al., First year Wilkinson microwave anisotropy probe (WMAP) observations: determination of cosmological parameters, Astrophys. J. Suppl. 148 (2003), 175-194, astro-ph/0302209.
    Tegmark M. et al., Cosmological parameters from SDSS and WMAP, Phys. Rev. D 69 (2004), 103501, 26 pages, astro-ph/0310723.
  19. Jassal H., Bagla J., Padmanabhan T., Observational constraints on low redshift evolution of dark energy: How consistent are different observations?, Phys. Rev. D 72 (2005), 103503, 21 pages, astro-ph/0506748.
  20. Chaves M., Singleton D., Phantom energy from graded algebras, Modern Phys. Lett. A 22 (2007), 29-40, hep-th/0603160.
  21. Cai R., Wang A., Cosmology with interaction between phantom dark energy and dark matter and the coincidence problem, J. Cosmol. Astropart. Phys. 2005 (2005), no. 3, 002, 17 pages, hep-th/0411025.
  22. Boucaud Ph. et al., Consistent OPE description of gluon two point and three point Green function?, Phys. Lett. B 493 (2000), 315-324, hep-ph/0008043.
    Boucaud Ph. et al., Testing Landau gauge OPE on the lattice with a áA2ñ condensate, Phys. Rev. D 63 (2001), 114003, 9 pages, hep-ph/0101302.
    Gubarev F.V., Stodolsky L., Zakharov V.I., On the significance of the vector potential squared, Phys. Rev. Lett. 86 (2001), 2220-2222, hep-ph/0010057.
    Gubarev F.V., Zakharov V.I., On the emerging phenomenology of á(Aa m)2minñ, Phys. Lett. B 501 (2001), 28-36, hep-ph/0010096.
  23. Kondo K.-I., Vacuum condensate of mass dimension 2 as the origin of mass gap and quark confinement, Phys. Lett. B 514 (2001), 335-345, hep-th/0105299.
  24. Faddeev L.D., Popov V.N., Feynman diagrams for the Yang-Mills field, Phys. Lett. B 25 (1967), 29-30.
  25. Li X., Shakin C.M., Description of gluon propagation in the presence of an A2 condensate, Phys. Rev. D 71 (2005), 074007, 13 pages, hep-ph/0410404.
  26. Dzhunushaliev V.D., Singleton D., Ginzburg-Landau equation from SU(2) gauge field theory, Modern Phys. Lett. A 18 (2003), 955-966, hep-th/0210287.
    Dzhunushaliev V.D., Singleton D., Effective 't Hooft-Polyakov monopoles from pure SU(3) gauge theory, Modern Phys. Lett. A 18 (2003), 2873-2886, hep-ph/0306202.
  27. Dudal D. et al., A determination of A2(m) and the nonperturbative vacuum energy of Yang-Mills theory in the Landau gauge, Phys. Lett. B 562 (2003), 87-96, hep-th/0302128.
  28. Feng B., Wang X., Zhang X., Dark energy constraints from the cosmic age and supernova, Phys. Lett. B 607 (2005), 35-41, astro-ph/0404224.
    Vikman A., Can dark energy evolve to the phantom?, Phys. Rev. D 71 (2005), 023515, 14 pages, astro-ph/0407107.
    Andrianov A., Cannata F., Kamenshchik A., Smooth dynamical crossing of the phantom divide line of a scalar field in simple cosmological models, Phys. Rev. D 72 (2005), 043531, 8 pages, gr-qc/0505087.
    Nojiri S., Odintsov S., Inhomogeneous equation of state of the universe: phantom era, future singularity, and crossing the phantom barrier, Phys. Rev. D 72 (2005), 023003, 12 pages, hep-th/0505215.
  29. Feng B. et al., Oscillating quintom and the recurrent universe, Phys. Lett. B 634 (2006), 101-105, astro-ph/0407432.
    Xia J., Feng B., Zhang X., Constraints on oscillating quintom from supernova, microwave background and galaxy clustering, Modern Phys. Lett. A 20 (2005), 2409-2416, astro-ph/0411501.
    Li M., Feng B., Zhang X., A Single scalar field model of dark energy with equation of state crossing -1, J. Cosmol. Astropart. Phys. 2005 (2005), no. 12, 002, 8 pages, hep-ph/0503268.
    Zhao G. et al., Perturbations of the quintom models of dark energy and the effects on observations, Phys. Rev. D 72 (2005), 123515, 16 pages, astro-ph/0507482.
    Xia J. et al., Observing dark energy dynamics with supernova, microwave background and galaxy clustering, Phys. Rev. D 73 (2006), 063521, 8 pages, astro-ph/0511625.
  30. Ahluwalia-Khalilova D.V., Grumiller D., Dark matter: a spin one half fermion field with mass dimension one?, Phys. Rev. D 72 (2005), 067701, 4 pages, hep-th/0410192.
    Ahluwalia-Khalilova D.V., Grumiller D., Spin half fermions with mass dimension one: theory, phenomenology, and dark matter, J. Cosmol. Astropart. Phys. 2005 (2005), no. 7, 012, 72 pages, hep-th/0412080.
  31. Wei Y., Big rip in SO(1,1) phantom universe, gr-qc/0502077.
  32. Wiltshire D., Exact solution to the averaging problem in cosmology, Phys. Rev. Lett. 99 (2007), 251101, 4 pages, arXiv:0709.0732.
    Wiltshire D., Cosmic clocks, cosmic variance and cosmic averages, New J. Phys. 9 (2007), 377, 66 pages, gr-qc/0702082.
    Wiltshire D., Gravitational energy and cosmic acceleration, arXiv:0712.3982.

Previous article   Next article   Contents of Volume 4 (2008)